Mathematics

# I need to solve this for r: r *squared* - 8r - 9 = 0

$r ^2 - 8r - 9 = 0 \\ r^2+r-9r-9=0\\ r(r+1)-9(r+1)=0\\ (r-9)(r+1)=0\\ r=9 \vee r=-1$
$r^2-8r-9=0\\\\a=1;\ b=-8;\ c=-9\\\\\Delta=b^2-4ac\\\\\Delta=(-8)^2-4\cdot1\cdot(-9)=64+36=100\\\\r_1=\frac{-b-\sqrt\Delta}{2a}\to r_1=\frac{-(-8)-\sqrt{100}}{2\cdot1}=\frac{8-10}{2}=\frac{-2}{2}=-1\\\\r_2=\frac{-b+\sqrt\Delta}{2a}\to r_2=\frac{-(-8)+10}{2\cdot1}=\frac{8+10}{2}=\frac{18}{2}=9\\\\Answer:r=-1\ or\ r=9.$